Question

Asked Feb 13, 2019

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What effect does standardizing into z-scores have on the spread (standard deviation) of a variable?

Step 1

**What is Z-score and standardized variables:**

*Z-score:*

The *Z*-score measures a particular value’s relationship to the mean in a group of values. It gives the number of standard deviation from the mean for the particular data point.

The general formula to obtain *Z-*score is,

*Z =* (*x – *population mean) / population standard deviation.

*Standardized variables:*

Standardized variables are the variables which are rescaled using the *Z*-score and these variables will have mean 0 and standard deviation 1.

Step 2

**Find the effect of standardizing into z-scores on the spread of a variable:**

From the definition of *z*-score and standardized variables, it is known that the standard deviation of the standardized variable will be equal to “1”.

That is, standardizing into *z-*scores changes the spread by making standard deviation as 1. Since, the units of the variable...

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